Abstract
We compare existence and uniqueness results for one dimensional current driven semiconductor models with those for a one dimensional semiconductor model subject to potential conditions. Furthermore, we discuss the reasons that for the bipolar current driven model it is physically not possible to impose the electron current I n and the hole current I p independently, but that only the total current I = I n + I p can be chosen. This introduces a coupling between the current continuity equations which is not present for the potential driven model.
Moreover, we examine the restrictions on the current I in the existence proof of solutions to the current driven model. Employing classical results on approximate physical models, we argue that the restrictions on the current I do not correspond to actual physical effects, but are rather due to some limitations of the techniques employed in the proofs.
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© 1990 Springer Basel AG
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Kerkhoven, T. (1990). Modelling of Semiconductors Subject to Prescribed Currents. In: Bank, R.E., Merten, K., Bulirsch, R. (eds) Mathematical Modelling and Simulation of Electrical Circuits and Semiconductor Devices. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 93. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5698-0_14
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DOI: https://doi.org/10.1007/978-3-0348-5698-0_14
Publisher Name: Birkhäuser, Basel
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